Defining parameters
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.n (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(80\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(175, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 248 | 184 | 64 |
Cusp forms | 232 | 184 | 48 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(175, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
175.4.n.a | $184$ | $10.325$ | None | \(0\) | \(0\) | \(-46\) | \(0\) |
Decomposition of \(S_{4}^{\mathrm{old}}(175, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)